DFT analysis of g and 13C hyperfine coupling tensors for model Ni(I)(CO)(n)L(m) (n = 1-4, L = H2O, OH-) complexes epitomizing surface nickel(I) carbonyls

Relativistic calculations within the spin-orbit mean-field (SOMF) approximation, the zero-order regular approximation (ZORA), and the scalar relativistic method based on the Pauli Hamiltonian were performed for the prediction and interpretation of the electronic g tensor and (13)C hyperfine tensor for a set of model polycarbonyl nickel(I) complexes with aqua or hydroxy coligands. They exhibit extensive similarities with heterogeneous [Ni(I)(CO)(n)]-surface complexes produced upon adsorption of carbon monoxide on Ni(I) ions grafted on silica or inside the zeolite channels. Benchmark calculations showing the influence of the exchange-correlation functional on the g tensor were carried out for well-defined nickel(I) complexes of known structure. On this basis, the SOMF-B3LYP scheme was chosen for calculations of the g tensor, and the obtained results were in satisfactory agreement with literature EPR data found for the [Ni(I)(CO)(n)]/SiO(2) system. The calculated g and A((13)C) tensors allowed polycarbonyl complexes of various stereochemistries to be distinguished. The nature of the Deltag(ii) shifts was assessed in terms of the molecular orbital contributions due to the magnetic-field-induced couplings and their structure sensitivity. The noncoincidence of g and (13)C hyperfine principal axes and their orientation with respect to the molecular framework was also examined. The ability of DFT calculations to follow consistently variations of the EPR parameters induced by stereochemical changes around the Ni(I) center provides an invaluable reference for the interpretation of experimental results.     

A combined experimental and quantum chemistry study of selenium chemical shift tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.     

Analyzing NMR shielding tensors calculated with two-component relativistic methods using spin-free localized molecular orbitals

A recently developed analysis method [J. Chem. Phys. 127, 124106 (2007)] for NMR spin-spin coupling constants employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs) has been extended for analyzing NMR shielding tensors. Contributions from a field-dependent basis set (gauge-including atomic orbitals) have been included in the formalism. The spin-orbit NLMO/NBO nuclear magnetic shielding analysis has been applied to methane, plumbane, hydrogen iodide, tetracholoplatinate(II), and hexachloroplatinate(IV).     

Spin-orbit configuration interaction study of the electronic structure of the 5f (2) manifold of U(4+) and the 5f manifold of U(5+)

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.     

Comparative study of relativistic density functional methods applied to actinide species AcO(2)(2+) and AcF(6) for Ac = U,Np

A two-component relativistic density functional method based on the Douglas-Kroll-Hess transformation has been applied to the actinyls and hexafluorides of U and Np. All-electron scalar relativistic calculations as well as calculations including spin-orbit interaction have been compared to results obtained with a pseudopotential approach. In addition, several exchange-correlation potentials have been applied to examine their performance for the bond lengths and vibrational frequencies of the title compounds. The calculations confirm the well-known accuracy of the LDA approach for geometries and frequencies, which is corroborated for the hexafluorides where gas phase experimental data are available. Comparison with results of accurate wave function based methods provides further confirmation of this finding. Gradient-corrected functionals tend to overestimate bond lengths and underestimate frequencies also for actinide compounds. The results obtained with Stoll-Preuss (small core) effective core potentials agree very well with those of all-electron calculations, while calculations with Hay-Martin large core pseudopotentials are somewhat less accurate. For all molecules and properties considered, spin-orbit effects have been found negligible concomitant with the closed-shell electronic structure of the U(VI) compounds and the open-shell situation of the Np(VI) compounds with a single valence f electron.     

水溶液中碳酸铀酰化合物的电子结构

应用相对论密度泛函理论系统研究了水溶液中非水合化和水合化碳酸铀酰化合物Cn/m(其中n和m分别为结构中碳酸配体和水配体的个数)的结构.溶剂效应采用类导体屏蔽模型(COSMO),并采用零级规整近似(ZORA)方法考虑标量相对论效应和旋-轨耦合相对论效应.电子跃迁采用包含旋-轨耦合相对论效应的含时密度泛函理论并在相关交换势中采用轨道势能统计平均(SAOP)做近似计算.结果表明碳酸配体对配合物结构和电子跃迁有很大的影响.C3/0配合物的稳定性可归于5f轨道参与了高占据轨道的成键作用.增加碳酸盐配体导致最大波长的蓝移,并在近可见光区域出现高强度的吸收.     

Remarkable interplay of electron correlation and relativity in the photodetachment spectrum of PtCl(6)2-

In this work we calculate the photoelectron spectrum of the PtCl(6) (2-) dianion by application of the recently developed third-order Dirac-Hartree-Fock implementation of the one-particle propagator technique allowing for a consistent treatment of spin-orbit and scalar relativistic effects together with electron correlation. For PtCl(6) (2-) a gas phase photoelectron spectrum is available showing clearly discernible structures not reproducible by a nonrelativistic or purely scalar-relativistic computation. A population analysis of the valence orbitals allows for an assignment of the photoelectron peaks and reveals the strong influence of relativity in combination with electron correlation.     

Interpreting Aromaticity and Antiaromaticity through Bifurcation Analysis of the Induced Magnetic Field

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non-aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring-shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring-shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring-shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e., in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity.     

Calculations of frequency-dependent molecular magnetizabilities with quasi-relativistic time-dependent generalized unrestricted Hartree-Fock method

The time-dependent generalized unrestricted Hartree-Fock (TDGUHF) method combined with a two-component quasi-relativistic Hamiltonian generated from the Douglas-Kroll-Hess (DKH) transformation was developed to calculate frequency-dependent molecular magnetizabilities, which are the linear response quantity of a molecule to an external magnetic field. By calculating the magnetizabilities of H(2)X (X = O, S, Se, and Te), the noble gases (He, Ne, Ar, Kr, and Xe) and small open shell molecules (CH(2), CH(3), and O(2)), we found that scalar relativistic terms affect mainly the diamagnetic magnetizability and spin-orbit (SO) interaction affects the paramagnetic magnetizability.     

Electronic structure and molecular properties of the heptacyanorhenate [Re(CN)7]3- and [Re(CN)7]4- complexes

We report scalar relativistic and Dirac scattered wave (DSW) calculations on the heptacyanorhenate [Re(CN)7](3-) and Re(CN)7(4-) complexes. Both the ground and lowest excited states of each complex split by spin-orbit interaction by about 0.3 eV. The calculated molecular electronegativities chi indicate that the open-shell complex is less reactive than the closed-shell complex, in agreement with experimental observations. The calculations indicate that the ground state spin density is highly anisotropic and that spin-orbit effects are responsible for the magnetic anisotropy of the molecular g tensor of the Re(CN)7(3-) complex. The calculated optical electronic transitions for both complexes with a polarizable continuum model using a time-dependent density functional (TDDFT)/B3LYP formalism are in reasonable agreement with those observed in the absorption spectrum.     

Analyzing molecular properties calculated with two-component relativistic methods using spin-free natural bond orbitals: NMR spin-spin coupling constants

An analysis method for static linear response properties employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic "natural localized molecular orbitals" (NLMOs) and "natural bond orbitals" (NBOs) has been developed. The spin-orbit NLMO/NBO analysis has been applied to study the indirect spin-spin coupling (J-coupling) constants in Tl-I, PbH(4), and a dinuclear Pt-Tl bonded complex with a very large Pt-Tl coupling constant (expt.: 146.8 kHz). For Tl-I it is shown that the analysis scheme based on scalar relativistic NLMOs is applicable even if spin-orbit coupling is responsible for most of the coupling's magnitude. For PbH(4) it is shown that electron delocalization plays a much larger role for the Pb-H coupling than it is the case for the C-H coupling in methane. For the Pt-Tl complex the analysis clearly demonstrates the strong influence of the ligands on the Pt-Tl coupling constant and quantifies the effect of the delocalization of the Pt-Tl bond on the Pt-Tl coupling constant.     

Theoretical calculation of the photodetachment spectra of XAuY- (X, Y = Cl, Br, and I)

The photodetachment spectra of the title molecules have been calculated, taking electron correlation and spin-orbit coupling into account and employing improved relativistic effective core potentials for gold and the halogen atoms. The calculated spectra have been compared with existing experimental spectra. The spin-orbit splitting of several degenerate electronic states has been calculated. The composition of the spin-orbit eigenstates are analyzed in terms of scalar relativistic electronic states. A comparison of the relative position of peaks in the calculated photodetachment spectra of the title molecules has been made.     

An investigation of lanthanum coordination compounds by using solid-state 139La NMR spectroscopy and relativistic density functional theory

Lanthanum-139 NMR spectra of stationary samples of several solid La(III) coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the 139La NMR spectra of the central transition are dominated by the interaction between the 139La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical-shift anisotropy on the NMR spectra is non-negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the 139La quadrupolar coupling constants (C(Q)) range from 10.0 to 35.6 MHz, the spans of the chemical-shift tensor (Omega) range from 50 to 260 ppm, and the isotropic chemical shifts (delta(iso)) range from -80 to 178 ppm. In general, there is a correlation between the magnitudes of C(Q) and Omega, and delta(iso) is shown to depend on the La coordination number. Magnetic-shielding tensors, calculated by using relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) and incorporating scalar only or scalar plus spin-orbit relativistic effects, qualitatively reproduce the experimental chemical-shift tensors. In general, the inclusion of spin-orbit coupling yields results that are in better agreement with those from the experiment. The magnetic-shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical-shift and EFG tensors in the molecular frame. This study demonstrates that solid-state 139La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.     

High-order electron-correlation methods with scalar relativistic and spin-orbit corrections

An assortment of computer-generated, parallel-executable programs of ab initio electron-correlation methods has been fitted with the ability to use relativistic reference wave functions. This has been done on the basis of scalar relativistic and spin-orbit effective potentials and by allowing the computer-generated programs to handle complex-valued, spinless orbitals determined by these potentials. The electron-correlation methods that benefit from this extension are high-order coupled-cluster methods (up to quadruple excitation operators) for closed- and open-shell species, coupled-cluster methods for excited and ionized states (up to quadruples), second-order perturbation corrections to coupled-cluster methods (up to triples), high-order perturbation corrections to configuration-interaction singles, and active-space (multireference) coupled-cluster methods for the ground, excited, and ionized states (up to active-space quadruples). A subset of these methods is used jointly such that the dynamical correlation energies and scalar relativistic effects are computed by a lower-order electron-correlation method with more extensive basis sets and all-electron relativistic treatment, whereas the nondynamical correlation energies and spin-orbit effects are treated by a higher-order electron-correlation method with smaller basis sets and relativistic effective potentials. The authors demonstrate the utility and efficiency of this composite scheme in chemical simulation wherein the consideration of spin-orbit effects is essential: ionization energies of rare gases, spectroscopic constants of protonated rare gases, and photoelectron spectra of hydrogen halides.     

A theoretical study of the excited states of AmO2n+, n=1,2,3

The ground and excited states of the AmO(2) (+), AmO(2) (2+), and AmO(2) (3+) ions have been studied using the four-component configuration interaction singles doubles, spin-orbit complete active space self-consistent field, and spin-orbit complete active space-order perturbation theory methods. The roles of scalar relativistic effects and spin-orbit coupling are analyzed; results with different methods are carefully compared by a precise analysis of the wave functions. A molecular spinor diagram is used in relation to the four-component calculations while a ligand field model is used for the two-step method. States with the same number of electrons in the four nonbonding orbitals are in very good agreement with the two methods while ligand field and charge transfer states do not have the same excitation energies.     

Relativistic calculation of nuclear magnetic shielding tensor including two-electron spin-orbit interactions

A relativistic calculation of nuclear magnetic shielding tensor including two-electron spin-orbit interactions is performed. In order to reduce the computational load in evaluating the two-electron relativistic integrals, the charge density is approximated by a linear combination of the squares of s-type spatial basis functions. Including the two-electron spin-orbit interaction effect is found to improve the calculation results.     

Accurate ab initio potential energy curve of F2. II. Core-valence correlations, relativistic contributions, and long-range interactions

The nonrelativistic, valence-shell-only-correlated ab initio potential energy curve of the F(2) molecule, which was reported in the preceding paper, is complemented by determining the energy contributions that arise from the electron correlations that involve the core electrons as well as the contributions that are due to spin-orbit coupling and scalar relativistic effects. The dissociation curve rises rather steeply toward the energy of the dissociated atoms because, at larger distances, the atomic quadrupole-quadrupole repulsion and spin-orbit coupling counteract the attractive contributions from incipient covalent binding and correlation forces including dispersion.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.